A pair of four dice is rolled together till a sum of either 5 or 7 is obtained. Then the % probabili

Question

A pair of four dice is rolled together till a sum of either 5 or 7 is obtained. Then the % probability that 5 comes before 7 is

Professor PC Thomas Classes · Answer

When a pair of dice is thrown the chances of getting sum 5 is $(1,4),(2,3),(3,2)$, $(4,1)$ and sum 7 is $(1,6),(2,5),(3,4),(4,3)$, $(5,2),(6,1)$\ Probability of getting sum 5 when a pair of dice is rolled $=\frac{4}{36}=\frac{1}{9}$\ Probability of not getting sum 5 or 7\ $=1-\frac{10}{36}=\frac{26}{36}=\frac{13}{18}$\ Required probability\ $=\frac{1}{9}+\frac{13}{18} \cdot \frac{1}{9}+\left(\frac{13}{18}ight)^{2} \cdot \frac{1}{9}+\ldots \ldots=\frac{1 / 9}{1-\frac{13}{18}}=\frac{2}{5}$.\